Unfortunately there is no paid version of browser extensions (that people pay to download). Apart from the donations way you mentioned, the only other way I see someone monetizing it is by getting consulting work. If you make a popular extension and clearly mention your site after the installation process, I would think people could contact you to build their own extensions.
The only company that has made any significant money from browser extensions is AdBlock Plus. Google (and other advertisers) allegedly paid AdBlock millions of dollars to whitelist their domains. Google saved an estimated $887 million by doing so!